Gem can also be shared. Bottle and Divine Rapier have some interesting rules about sharing that don't come up much: you can't pass off bottled runes, but you can pass a Bottle and your teammate can fill it with a rune, then use it. Divine Rapiers can only be shared if an ally dies and a teammate picks it up, in which case it can be shared only with the original owner.

Besides, like you said, all consumables (wards, courier, tangos, clarities...) can be traded.

The few exceptions to the rule are ring of regeneration, ring of health, sage's mask, void stone, and perseverance. the logic, I've inferred, being:

you only get regen, and no other stat. unlike, say, hood of defiance, which gives health regen, but also magic resistance. the exception here being perseverance, which while it gives +10 damage, that damage is muted, the regen isn't.

it can't be upgraded into other items by the person receiving it, and is sort of muted in that sense. otherwise you'd see some strategy of giving a pooling a carry rings of regen at the start of the game.

also, bottles that have a rune in them can't be shared. otherwise, with 0 to 3 charges, they can be given to and used by allies (or enemies!).